(2x+6)(3x-2)=0

Solution for (2x+6)(3x-2)=0 equation:

(2x+6)(3x-2)=0

We multiply parentheses ..

(+6x^2-4x+18x-12)=0

We get rid of parentheses

6x^2-4x+18x-12=0

We add all the numbers together, and all the variables

6x^2+14x-12=0

a = 6; b = 14; c = -12;
Δ = b2-4ac
Δ = 142-4·6·(-12)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-22}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+22}{2*6}=\frac{8}{12}
=2/3
$